Columbus and the Pinzón brothers step ashore on 12 October 1492 on an island in the Bahamas. They plant in the ground the royal banner of Spain, claiming the place for Ferdinand and Isabella. They name it San Salvador, after Jesus the Saviour. (It is not known which island they landed on, though one in the Bahamas now bears the name San Salvador.)

These are not the first Europeans to reach the American continent, but they are the first to record their achievement. Columbus believes that he has reached the East Indies. Greeted by friendly inhabitants of San Salvador, he therefore describes them as Indians - an inaccurate name which has remained attached to the aboriginal peoples of the whole American continent. By the same token this region becomes known to Europe as the West Indies.

A few days later the explorers sail on. They pass many more islands, giving each a new Spanish name, until they reach during November the most important landfall of their expedition - the large island of Cuba, which Columbus convinces himself to be Cipango. This is a place of marvels described by Marco Polo at the eastern extremity of Asia, usually now assumed to be Japan.

Beyond Cuba the next significant landfall is another large island which Columbus names after Spain itself - Española, or Hispaniola. On its shores the Santa Maria runs aground and is wrecked. Columbus decides to leave here a small colony of some forty men, with food and ammunition for a year, while he sails back to Spain with news of his achievement.

Returning with Vicente Yañez Pinzón in the Niña, Columbus reaches Palos on March 15 (amazingly the Pinta arrives in Palos later on that same day, after losing contact with the Niña a month earlier in an Atlantic storm). Columbus makes his way to the court of Ferdinand and Isabella in Barcelona, where he is received with every honour. He presents the monarchs with a few captured natives of the Bahamas and some gold treasure.

This is the high point of Columbus's career. Three more voyages to America lie ahead of him, and great achievements. But from now on misfortune, often deriving from his own inadequacy as a colonial administrator, increasingly blights his endeavours.

The explorer departs on his fourth and final voyage in May 1502. It is an almost unmitigated disaster, of storms, mutinies, rotting ships’ timbers. But somehow he limps home, yet again, to reach Spain in November 1504. Since 1492 he has spent half his time in the transatlantic places he so passionately believed in long before he found his way to them.

Even more significantly, he has made the Atlantic crossing seem just an arduous journey rather than a terrifying step into the unknown. Other navigators, sailing for other monarchs, are fishing now in his waters. It is a measure of this change that Columbus himself crosses the Atlantic successfully no fewer than eight times. In a few short years the New World has become linked to Europe in what is unmistakably a new era.

The Portuguese and India: 1497-1502

An important expedition to the east leaves Lisbon in 1497. In July Vasco da Gama sails south in his flagship, the St Gabriel, accompanied by three other vessels. In late November the little fleet rounds the Cape of Good Hope. Soon they are further up the east coast of Africa than Dias ventured ten years earler. In March they reach Mozambique. They are excited to find Arab vessels in the harbour, trading in gold, silver and spices, and to hear that Prester John is alive and well, living somewhere inland.

In the well-established Portuguese tradition, da Gama has on board a good supply of stone pillars. He sets one up in each new territory, to claim it for his king.

The real prize lies ahead, a dangerous journey away, across the Indian Ocean. At Malindi, on the coast of Kenya, a pilot is found who knows the route northeast to Calicut, an important trading centre in southern India.

After twenty-three days Calicut is safely reached. Da Gama is welcomed by the local Hindu ruler, who must surely wonder why his guest is so keen to erect a stone pillar.

Da Gama spends three months in Calicut before sailing back to Africa. Adverse winds extend the crossing this time from three weeks to three months, and before the African coast is reached many of the crew die of scurvy -- a first glimpse of one of the problems of ocean travel.

Da Gama arrives back in Lisbon in September 1499, more than two years after his departure. He is richly rewarded by the king, Manuel I, with honours, money and land. He has not managed to conclude a treaty with the ruler of Calicut. But he has proved that trade with the east by sea is possible. Manuel moves quickly to seize the opportunity.

Six months later, in March 1500, the king sends Pedro Cabral on the same journey. He takes such a curving westerly route through the Atlantic that he chances upon the coast of Brazil (an accident with its own significant results). This time a warehouse is established in Calicut, but the Portuguese left there to run it are murdered. To avenge this act, da Gama is sent east again in 1502. He bombards Calicut from mortars aboard his ship. With this clear evidence of Portuguese power a treaty becomes available.

These events, east and west in India and Brazil, provide the basis of the Portuguese empire, with all its rich opportunities for future traders and missionaries.

Vespucci and America: 1500-1507

In May 1501 an Italian navigator, Amerigo Vespucci, sets sail from Lisbon in the service of the Portuguese king. In the previous year a Portuguese ship (captained by Pedro Cabral) has touched land in Brazil in the region of what is now Salvador, and Vespucci himself has explored around the mouth of the Amazon.

Vespucci's present aim is to explore to the south. In doing so he hopes to find his way round the peninsula which - according to Ptolemy - forms the southeast extremity of Asia.

In January 1502 Vespucci reaches the bay of Rio de Janeiro, and continues on southwards to beyond the mouth of the river Plate. It is not known how much further Vespucci sails before turning home (his ships get back to Lisbon in July), but he has certainly reached a point sufficiently far south to make him query the conventional wisdom deriving from Ptolemy.

Vespucci comes to the conclusion which gives his voyage such significance. He now believes that this immensely long coastline is not that of Asia. It is a separate continent of its own.

Vespucci explains his new theory in a letter describing his recent voyage (together with earlier ones). It is printed in Florence, in 1505, with the Latin title Quatuor Americi Vesputii Navigationes ('Four Voyages of Amerigo Vespucci').

The letter is reprinted in Lorraine, in 1507, with a preface in which the editor floats an idea. Rather improbably (and most gratifyingly for any editor) this idea catches on. The editor proposes that the newly found land be named after Amerigo, his distinguished author. As a practical suggestion he puts forward a version of the name which looks good in Latin. He suggests that the place should be called America.

Balboa and the Pacific: 1513

The Atlantic ocean begins to acquire a western edge and a definable shape after the discovery of the Caribbean by Columbus in 1492, followed by the exploration of the coast of Venezuela by a Spaniard (Alonso de Ojeda) in 1499-1500 and then landfall in Brazil in 1500 by a Portuguese navigator (Pedro Cabral).

This coastline is still believed (following the theories of Ptolemy and Columbus) to be part of Asia. That theory is not necessarily disproved by news which begins to reach the Spaniards as they make contact with the Indians of central America. The Indians speak of another vast sea not far away to the west.

Such a sea, if this land is indeed Asia, would consist of a huge bay somewhere south of China. It becomes known as the mar del sur ('south sea'). To be the first to find it is any explorer's dream.

An expedition to find the south sea is mounted, in a mood of urgency, by Vasco Núñez de Balboa in 1513. Balboa is the governor of a Spanish colony which he has established, in 1510, at Santa María la Antigua on the west shore of the gulf of Uraba (a region known then as Darién). He comes to believe that the south sea, with its fabled riches, could be reached from here in a fairly short expedition with a force of 1000 fighting men.

Balboa conveys this opinion to the Spanish king, Ferdinand II. It is a move which proves his undoing. Ferdinand is so impressed by the prospect that he plans a much more ambitious colony (Balboa's settlement contains fewer than 400 Spaniards). The extended colony is to have a new elderly governor, Pedrarias Davila.

News of the impending arrival of his replacement prompts Balboa to rapid action, to secure any possible glory for himself. On 1 September 1513 he sets off westwards with a force of 180 Spaniards and 800 Indians.

Four weeks later, climbing to the top of a hill, Balboa sees the Pacific spread out before him. He makes his way down to the coast, in the Gulf of San Miguel, and there claims the entire sea for the Spanish king. When news reaches Spain, Balboa is appointed governor of the south sea and of Panama.

The appointment inflames Pedrarias, already furious at being upstaged by a much younger upstart. The rivalry between the men intensifies. It results in disaster for Balboa.

Late in 1518 Pedrarias arrests Balboa on a trumped up charge of treason. Frustrating his rival's right of appeal, Pedrarias has him hurriedly beheaded in January 1519.

As if this were not injustice enough, the poet Keats - in literature's most famous reference to the discovery of the Pacific - credits Balboa's great achievement to the wrong conquistador: 'Or like stout Cortez when with eagle eyes/ He stared at the Pacific - and all his men/ Looked at each other with a wild surmise - / Silent upon a peak in Darien'.

The lure of spice: 16th century

The wealth of the spice islands, first reached by Portuguese navigators sailing east, is the stimulus for all subsequent maritime exploration in the 16th century.

The magnificent achievement of Magellan, crossing an uncharted Pacific ocean in 1520-21, is part of an attempt to reach the spice islands in a westerly direction and thus claim them for Spain. Similarly the discoveries of Cartier and Hudson in Canada, and of Barents to the north of Russia, are by-products of expeditions to find a northwest and northeast passage to the Indies.

Magellan's theory: 1518

Ferdinand Magellan learns the craft of navigator, between 1505 and 1512, voyaging to and around the East Indies in the service of his native Portugal. In 1516 his request for promotion is refused by the Portuguese king, who informs him that he may offer his services elsewhere.

The only alternative employment for a man of his skills is with Spain, Portugal's great rival on the oceans. As it happens, Magellan now holds a theory which could prove greatly to Spain's advantage.

The pope has granted to Spain all newly found territory lying west of the Tordesillas line, and to Portugal everything to the east of it. In terms of modern longitude, the line is approximately 50° W. In 1518 Magellan persuades the Spanish king that the spice islands, or Moluccas, may be less than half way round the globe travelling west from the Tordesillas line. If that is the case, the islands would belong to Spain.

He is almost right. The longitude of the Moluccas is about 125° E. They are therefore 185° west of the Tordesillas line, or just 5° more than half way round the globe. Spain will have a valid case, for instruments of the time cannot be so precise. But first Magellan has to reach his destination sailing westwards.

Magellan and Del Cano: 1519-1522

With a fleet of five ships, carrying 265 men, Magellan sails in September 1519 from Seville. In mid-December he reaches Rio de Janeiro. For the next ten months he explores southwards along the coast, searching for a channel through to the 'south sea' (sighted seven years earlier by Balboa).

The broad estuary of the river Plate delays him, falsely raising his hopes, and it is not until October 1520 that he begins to explore west and then south through the straits which now bear his name. The fleet is now reduced to three ships. One has been wrecked on the south American coast. The captain of another deserts and sails home from the straits.

On November 28 the three caravels begin their journey across an unknown ocean. The crossing lasts ninety-nine days, without replenishment of food or water. The explorers finally make landfall, at Guam in the Marianas, on March 6. It has been three months of nightmarish deprivation, with the crew reduced in the end to eating leather from the rigging. But the sea itself has been sufficiently friendly for Magellan to give it a name which sticks - the Pacific ocean.

The next landfall is in the Philippines.

On the island of Cebu Magellan and his party rapidly convert the ruler to Christianity, beginning a Spanish link with the Philippines which will last until 1898. But in April Magellan is killed in a skirmish with natives on the island of Mactan.

He is already west (and slightly north) of his destination in the Moluccas, and he has achieved the hardest part of the undertaking - coaxing his often mutinous crews across a vast unknown expanse of ocean. But the glory of leading the first complete circumnavigation of the globe falls to one of his officers, Juan Sebastian del Cano.

Del Cano finally reaches Spain in September 1522 with a single ship (the Victoria, only survivor of the fleet of five) and seventeen Europeans from the original crew of 265, together with four Indians. He is granted by the Spanish king, Charles V, a suitable addition to his coat of arms - the device of a globe and the inscription Primus circumdedisti me (Latin for 'you first encircled me').

With this achievement, humans at last know the extent of the planet on which we live (Copernicus, at this same moment, is beginning to think the unthinkable - that it may indeed be only a planet). But the Pacific still has surprises in store.

Cartier and the Northwest Passage: 1534-1542

The two northern Atlantic kingdoms, France and England, look enviously at the wealth which Portugal derives from trade with the spice islands of the east. France is the first to seek a western route to the same pot of gold.

In 1534 the French king, Francis I, sends Jacques Cartier - with two ships and sixty-one men - to look for a northwest passage linking the Atlantic, above the continent of America, with the Pacific. Cartier discovers the great inlet of the St Lawrence river, which he hopes will prove to be the mouth of a channel through the continent. He postpones the exploration until the next summer and returns to France. Meanwhile he claims the whole region for his king, under the title New France.

In 1535 Cartier sails and rows his longboats up the St Lawrence as far as an island occupied by Huron Indians. They make him welcome and take him to the highest point on their island. He names it Mont Réal, or Mount Royal.

Cartier returns for a third visit in 1541-2. An attempt to found a colony comes to nothing. But his discoveries prompt the interest of French fur traders in these regions. In 1611 Samuel de Champlain establishes the beginning of a settlement on the same Huron island, today the site of Montreal. Three years earlier Champlain has formed a settlement at Quebec. Thus Cartier's search for a way through to the east lays the foundation, unwittingly, for the French empire in the west.

Northeast Passage: 1525-1556

While the French are searching for a way north of America to China and the Indies, others believe that there may be a possible route north of Russia. The Arctic waters of the Barents Sea have long been familiar to northern seamen. The Vikings penetrate these regions in the 10th century. Russian vessels trade by this route with Norway in the 14th century. In 1525 a Russian diplomat in Italy mentions the possibility that similar channels could perhaps be followed eastwards to China.

The same idea is also prompting interest in England. In 1553 an expedition sets out from the Thames to search for this supposed northeast passage.

The three ships of the expedition, under the command of Hugh Willoughby, are towed down the river. As they pass Greenwich Palace, they salute the ailing Edward VI (the 15-year-old king is within six weeks of his death). But the sky-blue uniforms of the crew put a smart gloss on great incompetence and lack of preparation. Six months later Willoughby, with two of his ships, is stranded for the Arctic winter on a bleak shore of the Barents Sea. With no suitable clothing or provisions, they starve and freeze to death.

Their gruesome end is known because Willoughby's body and his journal are recovered in 1555 by the captain of the third ship, Richard Chancellor.

Chancellor's voyage of 1553 is, by accident, as successful as Willoughy's is disastrous. Separated from the other two ships in a storm, he continues his journey alone and reaches Kholmogory (upstream from the later town of Archangel). He is warmly welcomed and is invited to travel overland to visit Ivan IV (or Ivan the Terrible) in Moscow. So while Willoughby is perishing on the northern coast, Chancellor spends the winter at the tsar's lavish court (of which his detailed description later astonishes his compatriots at home).

In the spring of 1554 Chancellor rejoins his ship at Kholmogory. He arrives back in England during the summer.

Chancellor brings with him an offer from Ivan III of favourable trading terms for English ships and merchants. The result, in 1555, is the founding of the Muscovy Company. It is the earliest of the English chartered companies which are granted monopolies by the crown to develop trade with specific regions (others being the East India Company and the Hudson's Bay Company). A flourishing trade with Russia, mainly through the port of Archangel (founded in 1584), is the result of England's quest for the northeast passage.

Chancellor makes further voyages to Russia in 1555 and again in 1556, when he takes on board a Russian ambassador to England - but his ship is wrecked, with the loss of most of those on board, off the coast of Scotland.

Willem Barents: 1594-1597

The ending of Dutch trade with Portugal, in 1580, causes the merchants of Amsterdam to be as interested as their London counterparts in a northeast passage to the east. In 1594, and in each of the two succeeding years, an expedition is sent into Arctic waters under the command of Willem Barents.

In 1594, and again in in 1595, Barents reaches the coast of Novaya Zemlya but fails to find a channel through to the Kara Sea. In 1596 he takes a more northerly route. On this occasion he sights both Bear Island and Spitsbergen and makes his way round the northern point of Novaya Zemlya. There the ice closes in and traps his ship.

Barents and his companions survive the winter, becoming the first Europeans to do so within the Arctic circle. But the thaw in the spring is insufficient to free the ship. Barents decides to escape southwards in two open boats. After a week at sea, he dies. But most of his crew make their way back to the Netherlands.

Barents' gallant failure diverts Dutch attention to the southern route to the east. But they retain an interest in a possible northern passage. In 1609 the Dutch East India Company commissions an experienced English explorer, Henry Hudson, to make another attempt on its behalf.